Ionography imaging chamber

ABSTRACT

An imaging chamber for an x-ray system using a dielectric receptor sheet in the gap between electrodes. In one embodiment, a chamber with planar or cylindrical low conductivity electrodes having the conductivity per unit area varying from a central zone to the edge of each electrode to produce electrostatic potentials at the gap surfaces the same as the electrostatic potentials of concentric spherical metal electrodes. In another embodiment, a chamber with planar or cylindrical metal electrodes and dielectric sheets at each electrode to produce the desired potentials.

United States Patent [191 Proudian et al.

[ 1 Jan. 7, 1975 IONOGRAPHY IMAGING CHAMBER [75] Inventors: Andrew P. Proudian, Chatsworth;

Teodoro Azzarelli; Murray Samuel Welkowsky, both of Los Angeles, all of Calif.

[73] Assignee: Xonics, Inc., Van Nuys, Calif.

[22] Filed: Aug. 14, 1973 [21] Appl. No.: 388,212

Related US. Application Data [63] Continuation-impart of Ser. No. 319,999, Jan. 2,

1973, abandoned.

[52] US. Cl. 250/315, 250/374 [51] Int. Cl. G0lt 1/18 [58] Field of Search 250/315 A, 374, 375

[56] References Cited UNITED STATES PATENTS 2,606,295 8/1952 Scherbatskoy 250/374 2,692,948 10/1954 Lion 250/374 X 3,508,477 4/1970 Groo 250/315 X 3,710,125 1/1973 Jacobs et al. 250/315 A X Primary Examiner-Archie R. Borchelt Attorney, Agent, or FirmHarris, Kern, Wallen & Tinsley [57] ABSTRACT 15 Claims, 10 Drawing Figures 1 IONOGRAPHY IMAGING CHAMBER 1972, U.S. Pat. No. 3,774,029, entitled Radiographic- System with Xerographic Pringing, and assigned to the same assignee as the present application. in such a radiographic system, an X-ray opaque gas is used be-.

tween two electrodes in an imaging chamber to produce a photoelectric current within that chamber which is collected on a dielectricsheet placed on one or the other of the electrodes, resulting in a latent electrostatic image. The latent image is then made visible by Xerographic techniques. Collection of the primary photoelectrons created by the X-rays absorbed in the interelectrode gas filled gap and of the secondary electrons created by collisions of the primaries with the gas atoms is achieved by use of an accelerating potential difference, typically of the order of a few to ten kilovolts, applied between the electrodes.

In the current systems, the gas in the interelectrode gap plays two essential roles, namely, first as a maxima l ffi em b9 ofXjaysr tdicr.tqa h high sensitivity of the imaging technique, and second, as a means of stopping the primary electrons and creating secondaries in as short a distance from their point of creation as possible, in order to preserve the resolution of the imaging system. For both the above reasons, the gas selected is a high Z gas, such as Krypton or Xenon, contained in the interelectrode gap at high pressure, typically twenty atmospheres or more.

The manimum gas pressure in the gap is limited essentially by the increasing difficulty of containing the gas within a chamber with X-ray transparent walls, as

the pressure i s iii creased. For agiven gasp rssure, increased absorption can be achieved by increasing the interelectrode gap width. There is then a resultant small increase in the lateral diffusion of the electrons as they travel towards the collecting electrode. However, the spot size due to diffusion is actually very small, for gap pressure of 20 atmospheres or more, even for gap widths of 1 cm. or more. The limiting factor in system image resolution is not the electron diffusion, but rather the geometric unsharpness resulting ooms 9Pli9lE iH9 dn9Q QKQQ-Lw 9119 5919112 gap.

This is illustrated in FIG. 1, which shows the increasing degradation of resolution with deviation of the xrays away from normal incidence. X-rays incident along the central ray line AA create photoelectrons along the line AA which are multiplied in the gas (by the creation of secondaries) and are accelerated by the electric field E which is normal to the anode and cathode, and thus parallel to the line AA. The electrons are collected at the receptor in a spot around the point A, whose width is small and determined by the range of the primary photoelectrons and by diffusion of the secondaries. Typically the effective spot diameter due to those effects will be less than 0.1 mm. The charge distributioncollected around the point A will have a maximum at A, and fall off with distance away from the point, as depicted schematically in FIG. 2.

On the other hand, X-rays incident along the line O BB traverse the gas at an angle 0 to the normal vector of the planes of the electrodes, and therefore to the field E, and the electrons created along BB, are collected not just around the point B but around the line BB, where B" is the projection on the receptor of the point B, along the direction of E. Because of attenuation of the X-ray beam by the gas in traversing the gap along BB, there will be more charges collected around B than B", and the resultant charge image of the ray OBB is depicted schematically in FIG. 2, where it is seen that a geometrically unsharp image, weighted more heavily towards B and less towards B, but extending from B to B, results from absorption of the ray OBB. I

For a ray incident at angle 0, and for an interelectrode gap width d, the extent of the unsharp image will be proportional to 0 d for practical values of gap width and pressure (for which the X-ray absorption mean free path l/u, where p. is the X-ray attenuation coefficient, is such that p.d l Thus geometric unsharpness can be reduced by reducing either 0, which implies re duction of field size, since the maximum of 6 is equal to the ratio of maximum image radius to the so-called film-to-focus-distance, or by reduction of gap width d, which would result in decreased absorption of the incident X-rays, and hence a loss of quantum efficiency or sensitivity of the system.

The fundamental source of geometric unsharpness in the electrostatic latent image formed on the receptor is the lack of coincidence between the line along which incident X-rays create photoelectrons, and the field lines which accelerate those electrons to the receptor. Since the electron creation paths are portions of straight lines or rays all pointing to a common center, viz. the X-ray source, then to avoid geometric unsharpness the electric field lines in the gas gap should also be portions of rays pointing to the same center. More precisely, this means that the equipotential surfaces of the electrostatic potential in the gas gap must be portions of concentric spheres centered at the X-ray source. This would be the case if the electrodes of the imaging chambers or rather the inner (gap facing) surfaces of those electrodes, which form the boundaries of the gas gap, were portions of concentric spherical shells, with centers at the nominal assumed position of an X-ray source, so that the electric field between the electrodes would be radial, with all the field lines (or rather the extensions of the field lines beyond the electrodes), passing through the common center of the spherical shell electrodes. With such a configuration, as depicted in FIG. 3, and providing the X-ray source is in fact placed at the common center of the concentric electrodes, all the lines AA, BB along which primary electrons are created will be field lines, and the electrons will thus be accelerated along the same lines along which they were created, with resultant point images, of dimensions determined only by electron range, and not suffering from geometric unsharpness.

While the above solution to the problem of unsharpness by using concentric spherical cap electrodes may be possible, it suffers from significant drawbacks, the most important of which is the difficulty oif making flat images with spherical electrodes. If the dielectric receptor which must receive the latent electrostatic image is flat, it is quite difficult to stretch it on a spherical surface which is topologically different from a flat or cylindrical surface, so that it is necessary that the surface be elastically and unequally stretched to conform to a spherical shape. The difficulty is aggravated by the fact that this must be accomplished inside a pressure vessel with only a few millimeters between its walls. If a permanently mounted dielectric is used as the receptor of the latent images, on which the visible image is first formed, then one is faced with the problem of transferring the visible image formed on that receptor to the final receptor which must be flat. This again is quite difficult to realize in a practical system.

To summarize, a flat parallel electrode image chamber has the advantage of ease of mounting of the dielectric receptor and more generally of practicality but suffers from geometric unsharpness. On the other hand, a chamber with spherical electrodes overcomes the problem of geometric unsharpness but is difficult to implement in a practical system. It is desirable in some applications to make the imaging chamber electrodes cylindrical, because of added mechanical strength of such a configuration and for ease in applying the receptor to the electrode surface. A cylindrically curved surface is topologically equivalent to a flat surface so that no stretching of a flat receptor is required, while the curvature allows a roll fed receptor to be pulled into contact with the curved surface more readily than with a flat surface. The electrode surfaces at the gap in the cylindrical configuration usually will be portions of coaxial cylinders, with their common axis passing through the X-ray source. The equipotential surfaces in the gas gap of an imaging chamber with coaxial cylindrical electrodes are also portions of coaxial cylinders, and therefore a geometric unsharpness problem similar to the one existing for flat parallel electrodes will also exist for the cylindrical electrode case. Accordingly, it is an object of the present invention to provide a means of overcoming the problem of geometric unsharpness due to oblique X-ray incidence while at the same time retaining a flat or cylindrical surface for mounting the latent image dielectric receptor.

The present invention uses an imaging chamber with physically flat or cylindrical electrical conductor electrodes which provide an electric field in the gap between the electrodes corresponding to that of concentric spherical electrodes. This is accomplished in one flat electrode embodiment by using low conductivity electrodes with radially varying resistance and maintaining an appropriate potential difference between the center and outer edge of those electrodes at each electrode surface. In the corresponding cylindrical electrode embodiment, the resistance is varied axially along the gap, with a potential between the center and opposite curved edges.

More specifically, the conductivity per unit area of each electrode is varied from a central zone to the edge of the electrode, as by varying the thickness of the electrode and/or by varying the conductivity of the electrode material.

In one alternative embodiment, the desired electrostatic potential is approximated by forming each electrode as a plurality of concentric rings or parallel strips of different conductivities. In another alternative embodiment, dielectric sheets are placed over metal electrodes, with the dielectric constant varied from the central zone to the edge. Other objects, advantages, features and results will more fully appear in the course of the following description.

IN THE DRAWINGS FIG. 1 is a diagram illustrating operation of an imaging chamber with plane parallel electrodes;

FIG. 2 is a diagram illustrating the charge distribution for the configuration of FIG. I;

FIG. 3 is a diagram similar to that of FIG. I illustrating concentric spherical electrodes;

FIG. 4 is a diagrammatic illustration of an x-ray system with an imaging chamber incorporating the presently preferred embodiment of the invention;

FIG. 5 is an enlarged view of the imaging chamber of FIG. 4;

FIG. 6 is a schematic of the equivalent circuit diagram of the imaging chamber of FIG. 5;

FIG. 7 is a perspective view looking down on a cylindrical cathode, illustrating an alternative embodiment of the invention;

FIG. 8 is a view similar to that of FIG. 5 showing an alternative embodiment;

FIG. 9 is a view similar to that of FIG. 7 showing the alternative embodiment of FIG. 8 applied to a cylindrical electrode, and

FIG. 10 is a view similar to that of FIGS. 5 and 8 showing another alternative embodiment.

The system as illustrated in FIG. 4 includes an X-ray source 10 positioned for directing radiation to an 0bject 11 which may rest on a table 12. An imaging chamber 13 carrying the sheet receptor 14 may be positioned below the table, with X-rays from the source 10 passing through the object 11 and into the gas filled gap 15 of the imaging chamber I3. The design of the imaging chamber itself is not a feature of the present invention and various of the presently known imaging chambers may be utilized, including that illustrated in the aforementioned copending application.

The imaging chamber may comprise a housing 20 with a high resistance cathode 21 carried therein on an insulating sheet 22. The housing cover 23 may serve as the electrical ground, with the center 25 of the high resistance anode 24 connected to the cover through a fine conducting (e.g., aluminum) wire or thin strip 26. The anode is otherwise attached to the housing cover by a thin adhesive insulator 27, so that it is in electrical contact with the cover only through the strip or wire 26. Conductive strips 28 and 29 are attached to the outer edges of the anode and the cathode, respectively, so as to make good electrical contact all around the edges of the electrodes. The outer edge of the anode is electrically connected via the strip 28 to the center 30 of the cathode, through a variable resistance 31. The outer edge of the cathode is connected via the strip 29 to a power supply 32. The other terminal of the power source 32 is grounded or equivalently connected to the housing cover 23.

The electrical circuit formed by the above arrangement is shown schematically in FIG. 6. The chamber may also include means (not shown) for introducing a gas under pressure into the gap. The imaging chamber of FIG. 4 is utilized in the same manner as in the prior art devices described in the aforementioned copending application, and differs from the prior art devices in the electrode construction.

As previously mentioned. it is necessary in order to align the electric field lines within the imaging chamber tered' at the X-ray source. It is known, however, from electrostatic field theory, that in anyregion free of net charge, the electrostatic potential .0, and;its gradient E theiequipotential V 0 which is by definition the electric field vector,

are completely determined inside any region by speciwhere 0' (r) is the derivative of the potential 0 (r) with respect to r, and I is a constant which is equal to the current flowing across any closed contour on the disk.

fying the value of 6 on the boundaries of thatregion,

and of course by specifying the variation of dielectric permittivity e within that region. The permittivity of the gas gap is essentially unity. i ,f v

In application to the problem of the flat, plane parallel electrode imaging chamber'in electron radiography as depicted in FIGS. 4 and 5, this means that if the potential on the surfaces S and S bounding the gas gap (the gap being much smaller than the electrode dimensions, the edge effects due tothe f niteness of the elec'g trode surfaces areinegligible) is specified, theelectrostatic potential and electric field within the gas gap are uniquely and completely determined. 1'

Therefore; if it is desired that-jthe'equipotential surfaces within the flat gas gapbe portions ;of spherescentered at the X-ray source, it isonly necessaryiand sufficient that the electrostatic potentialstl fla nd 0 on the surfaces 8, and S be such'as' 'tocorrespondto such equipotentials. In other words," the surfaces S andS would not be equipotential surfaces ,(the'equipote'ntials Equation (3) shows that in order to obtain a particular variation 0 (r) of the potential across the electrode, one, can vary either the conductivity 0 (r), the thickness t (r), or both, of each electrode in such a manner the Eq. (3) is satisfied.

The power P dissipated in the conductor due to the current flowing through it, is easily shown to be the product ,Fo otential f the form of Eqs. (1 or (2), namely f )=V,,D/d(l.+ /D )1/2 "the derivative or electric field will be:

are spherical), and the values of 6 and 0 fat given points on S and S would be functions of the locationv of those points. In fact, if the positionof pointslP, and P on S and S were labeled by the polarcoordinates r, and r respectively, and the 'equipotentials 's'ought were concentric spheres with their centers a distance D and D+d from the surfaces 8, andS respectively, the variation of the potentialson S and S as functions of r and r respectively, must be where V, is the voltage'drop across the gap at the gap center and D D+d. i

The desired variation of electrostatic potential along the surfaces 8, and S as defined in equations (1.)"and (2), can be achieved by use of variable resistivityelectween different points on their surfaces. Naturally, there will be a current flow along the electrodes as aresult of the applied potential. The mathematical analysis I of the problem is straightforward, and is. sketched below: e 7 v Consider a conductor in the'shape of a circulardisk i of variable thickness t(r) and conductivity o"- (r) .where r is the radial polar coordinate measuredfrom the center of the disk. The disk center, up to a radius r,,, ises-l sentially a perfect conductor (e.g., made of aluminum).

the material are related by the approximate equation: it

trodes which can supporta potential difference be I from 2 10-1" ohm (l r /D As an example of a typical setof parameters let us choose V 10,000 volts, and I=l milliampere, and 30.

'mogeneous, i.e., o'(r) is a constant, o(r) 0",, 10 ohm cm and only the thickness varies, and select consider-the case'where the conductor electrode is ho- 'r, i 3; cm/D 100 cm and d=l cm. We find from Eqs.

(3) and (5) that the thickness of the conductor electrode must vary from t(r,,) '=200p.to t (r,,,) 811.. The 'total power dissipated, as computed from Eq. (4), is around 5 watts, which over a typical exposure time of 1/10 secondrepresents anegligible amount of heating. Alternatively, a conductor electrode of uniform thickness and variable conductivity material may be used..Then, for the above example, assuming the uniform thickness to' be 40h, the conductivity must range cm at r, to 5X10 ohm cm Manymaterials are available in the preferred range of conductivitiesbetween 10 ohm cm and 10' ohm cmfflincluding chalcogenide glasses (e.g. A5 Se andcarbon impregnated plastics (e.g., thermosetting epoxy resin with'acetylene black), the latter being preferable. for ease of tailoring and forming, and weak temperature dependence of the conductivity. These materials can be cast in molds or machined to thedesired thickness, and their conductivity can be varied from center to edge by variation of their composition (e.g., by varying the conductivity and/or loading of the carbon black filler in the material). If conductors ofnonuniformthickness are used, the insulating substrate to which they are attached would be given a reverse curvature to insure thatthe gap side of the electrode be flat, though small deviations from flatness are not serious. .The variation of thickness and/or conductivity along the electrodes would be very nearly the same for the anode and the cathode, since the potentials along the -two electrodes have the same form, and differ only by the substitution of the length (D+d) for the length D between Eqs. (I) and ('2).

For the typical example given above, the potential change between the center and the periphery of let us say the anode is approximately 5000 volts, and the total resistance R between the anode center and periphery is approximately megohms. The periphery of the anode would then be connected to the center of the cathode through an additional 5 megohm resistor (the variable resistance 31 of FIG. 6), and the applied potential V required between the cathode periphery and the anode center to produce a gap voltage of 10,000 volts at the gap center is 15,000 volts.

Similar considersations apply to the case of coaxial cylindrically curved electrodes centered at the X-ray source. The radii for the cylindricalelectrodes are large and the figures of the drawings also illustrate this embodiment, with the cylindrical axis perpendicular to the paper. A perspective view of a cylindrical cathode is shown in FIG. 7, on a reduced scale. In coaxial cylindrical case, it is easily shown that the electric potential at any point p on the cylindrical surface must vary according to the law where Vg is gap voltage as before,

D is the cylinder radius,

d is the gap width,

D is the sum of D d, and

Z is the axial coordinate of the point p, that is, the coordinate measured along the cylinder axis from the center or middle of the cylindrical cap which forms the electrode, corresponding to r or Eq. 1 and 2. Thus there is only an axial dependence of the potential for the case of cylindrical electrodes. The equation corresponding to Eq. (3) and relating electrode conductivity, thickness and the derivative of the electrostatic potential for the case of the cylindrical electrodes is S t(Z) o-(Z) 0(Z)=I s) where S is the arc length of the cylindrical section constituting the electrodes, and of course the thickness t and conductivity 0' of the electrodes are functions only i of the axial coordinate Z. The required values of the electrode thicknesses, material conductivities, and the resultant current and power dissipation values are of the same magnitude as the case of flat electrodes.

The electrical connections with thecylindrical electrodes are basically the same as the case of flat electrodes: the central disk of perfect conductor of each electrode is replaced by a central arcuate strip (30' in FIG. 7) of perfect conduction a few centimeters in width, and the two arcuate edges (29' in FIG. 7) of the electrode are connected electrically to each other. The arcuate edges of the anode are connected through the variable resistance 31 to the central arcuate strip on the cathode 21. The arcuate edges of the cathode 21 are connected through the power supply 32 to the central strip of the anode 24. In a typical example, D may be in the order of 2 meters,,so that the edge of a 12 inch wide electrode will be about a millimeter out of plane. The expression substantially planar is intended to cover such a structure, referring to both the flat and cylindrical embodiments.

The use of what might be termed virtual curved electrodes still implies that the field lines and the path of creation of primary photoelectrons in the gas gap are only coincident if the X-ray source is placed at the center of the virtual concentric electrodes.

The central zone with uniform high conductivity per unit area is preferred by not essential. This zone is the disk in the flat electrode embodiment and the strip in the cylindrical electrode embodiment. The problem due to the oblique path of the X-rays is minimal or nonexistent in the central zone. This zone of high conductivity provides a good surface for electrical wire connection and also simplifies the electrode manufacturing process.

An approximation of the desired ideal concentric spherical potential variation can be achieved by means other than continuous variation of the conductivity and/or thickness of the electrodes. For example, a plurality of concentric annular rings, each of constant conductivity, can be used to form an electrode, with the conductivity of each ring from the center to the edge being selected at a value such that the potential variation along the radial coordinate will approximate in a stair-step fashion, the desired ideal potential variation.

A pair of electrodes 21, 24 incorporating this construction is shown in FIG. 8, with elements corresponding to those of FIG. 5 having the same reference numerals. In the electrode 24', a plurality of concentric rings 40-45 are positioned about the conductive center 25, extending to the conductive edge 28. A similar construction is provided for the electrode 21, with concentric rings 46-51. Each of the rings 40-5l will be of low conductivity material, as used in the embodiment illustrated in FIG. 5. Each ring will have a uniform conductivity, but the conductivity will vary from ring to ring. to approximate the desired relationship discussed above. In the embodiment illustrated in FIG. 8, only six rings are shown for purposes of clarity. A typical imaging chamber might utilize I5 rings each inch wide.

The approximation configuration of FIG. 8 is suitable for use with the cylindrical electrode configuration of FIG. 7, and a corresponding structure is shown in FIG. 9. In the electrode 21' of FIG. 9, strips 46' 51' are provided between the center 30' and edges 29'. Each of the strips 46 51' is of constant conductivity, with the conductivity of adjacent strips chosen to provide the stair-step approximation to the desired ideal potential variation.

In another alternative embodiment, the desired electric field is accomplished by utilizing metal electrodes, typically aluminum or beryllium, with dielectric sheets of uniform thickness at each electrode surface with each sheet comprising at least two different dielectric materials. One such configuration is illustrated in FIG. 10 with elements corresponding to those of FIG. 5 identified by the same reference numerals. The dielectric embodiment is also applicable to the cylindrical configuration of FIG. 7. A dielectric sheet 60 is carried on the electrode 24a and another dielectric sheet 61 is carried on the electrode 21a.

The desired variation of electrostatic potential along the bounding surfaces S and S of the gas gap can be achieved by the use of the composite dielectric sheets 60, 61 between the plane electrodes 24a, 21a and the gas gap surfaces 8,, S The dielectric sheet consists of improvement comprising:.

a pair of dielectric inserts 60a, 60b of variable thickness I andof uniform but unequal dielectric constants e3 e Thedielectric sheet 6-l similarly-consists of a pair of dielectric inserts 61a, 61b of -variab le, thickness and of uniform but unequal dielectric constants 62 ,2

The dielectricconstants e e, and e e are selected so that the desired electrostatic potentials are realized at the surfaces S and S The total thicknessof dielecface S and electrode2la. Dielectric sheet 60 has thickness T with layers 60a,60b of thickness 2 t respectively. Dielectric sheet 61 has thickness T with layers 61a, 61b of thickness t respectively. The iridividual thicknesses t t a'nd't are functions of r,

and r respectively, such th'atthe desired potential at S,

and S are realizedvThe boundaries b, and b between i the dielectric layers are not plane of course, but arelde termined by the required potential distributions.

The exact shapeof the boundaries b, and b or more (r of the thickness of dielectric layers 60a, 61a, as well as the total thicknesses T, and'T may be obtained by numerical computation (to solve for the boundaries which will yield the desired'solution of the governing. La Place equation); Qualitatively, however, each composite dielectric sheetconsists in one embodiment of an inner layer (i.e.-,-adjjacent to the electrode) of relatively higher dielectric' constant e, of maximum thicknesst (0) at the center, tapering down to a minimum thicknesst (p max) at the edge of the field of view, and

of an outer layer of complimentary thickness (such.

that t t T,) and of lower dielectric constant e,' e,. The structure between electrodeZla and surface S would be similar. Variations on thisv structure are possible, in particular by inverting the inner and outer dielectric layers. 3

Alternatively, the desired v achieved by means of a ,s'ingleflay'e'r'inthe dielectric sheet with a variable dielectricconstantLTheoperation of the embodiment with the dielectric sheets is similar to that of the embodiment withthelowlconductivity electrodes," except-that the effectiveisurface charge generated by the current flowing in theconductor, is re-; placed by static-polarizationcharge, The-dielectric em bodiment has a disadvantage in that the thickness of dielectric required in most applications is such as to'tefnd potential variation may be i simply, the exact functional dependences t (r and t 1 Q I with said means for connecting including circuit means for connecting the power supply to the center of said first electrode and to opposite edges of said second electrode, and I with said meansformaintainin'g including a resistance connected between opposite edges of said first electrode and the center of said second electrode completing a'current path across the power supply to producean electrostatic field in the gap, with the conductivity per unit area of each of said .=electrodes varying from a central zone to said ledges such, that the electrostatic potential at the "gapv surfaces of .the electrodes is the same as the electrostatic potential for concentric spherical -'metal electrodes. ,,3- In an imaging chamber for an X-ray system, the

I improvement comprising:

first and second substantially planar electrodes, means for mounting said electrodes in the chamber in spaced relation defining a gap therebetween; means for connecting a power supply across said electrodes; and

i. means for maintaining along the gap surfaces of said electrodes, electrostatic potentials corresponding to the electrostatic potentials for concentric spherical metal electrodes, with the electrostatic potentials 0, and 6 at the gap surfaces of the electrodes substantially 1 (P1) g l+x12/D2)l/2 2 (P2) gD' 2 where p is the position on the electrode gap surface, V

is the voltage drop across the gap at the gap center, D is the distance from one electrode gap surface to the x-ray source, d is the distance between electrode gap surfaces, D D+d, and x is the distance of p from the 7 gap center in ,polar' coordinates for flat electrodes and from thegap centerfor cylinimprovement comprising:v

to build up a significant counterfield as the collected charge due to the image build up. Also, control of dielectric constant in presently available material iscor siderably more difficult than control We claim: 1. In an imaging chamber means for connecting a powersupply' .across said:

electrodes; and

for an X-ray systempth e V 'ofconductivityq electrodes, electrostatic potentials corresponding to the electrostatic potentials for concentric spherijcal metal electrodes so that, the. electric field lines I-i in said gap converge substantially to a'point.

material,

firstand'lsecond substantially planar electrodes;

means for mounting said electrodes in the chamber in spaced relationfdefining a gap therebetween; means for connecting a power supply across said electrodes; andmeans for maintaining along thegap surfaces of said electrodes, electrostatic potentials corresponding to the electrostatic potentials for concentric spherical metal electrodes, with each of said first and second electrodes comprising a plurality of sections of low conductivity material, with each section of different and substantially uniform conductivity, with said means for connecting including circuit means for connecting the power supply to the center of said first electrode and to opposite edges of said second electrode, and

a, I 2 fwith said means for maintaining including aresismeans for maintaining along the gap surfacesof said:

1' tance connected between opposite edges of said first electrode and the center 'of said second electrode completing a current path across the power I ,'supply to produce an electrostatic field in the gap, with thefconductivity per unit area of each section of -said electrodes-varying from a central zone to said edges such that the electrostatic potential at the ggap surfaces of the electrodes corresponds step- 1 1 wise to the electrostatic potential for'concentric spherical metal electrodes.

5. An imaging chamber asdefined in claim 1 wherein said electrodes have flat parallel gap surfaces and a central disk of high conductivityma terial. v

6. An imaging chamber as defined in claim 1 wherein said electrodes have concentric cylindrical gap surfaces and acentral arcuate strip of high conductivity material.

7. In an im r t t t qm si a a g f' st and second substantially planar electrodes;

means for mounting said electrodes in the chamber in spacedrelation defining a gap therebetween; means for connecting a power supply across said electrodes; and means for maintaining along the gap surfaces of said electrodes, electrostatic potentials corresponding to the electrostatic potentials for concentric spherical metal electrodes, 1 with said electrodes-of metal, and with said-means for maintaining including first and second dielectric sheets, each of uniform thickness, with said first sheet at said first electrode and said second sheet at said second electrode'defining a gap betweenthe sheets, each of said sheets having a dielectric constant varying across the sheet such that the electrostatic potential at the gap surfaces is the same as the electrostatic potential for concentricspherical metal electrodes. 5 8. A system as defined in claim 7 wherein each of said sheets comprises a first layer of a first dielectric conimaging chamber for an X-ray system, the

stant and a second layer of a second dielectric constant, v

with one of said layers having a maximum thickness at the center thereof and tapering to a minimum thickness at the edges thereof, and with the other of said layers having a complementary thickness.

9. In an imaging chamber for an X ray system, the

improvement comprising:

first and second substantially planar electrodes of low conductivity material; means for mounting said electrodes in the chamber in spaced relation defining a gap there between;

means for connecting a power supply to the center of said first electrode and to opposite edges of said second electrode; and

a resistance connected between opposite edges of said first electrode and the center of said second electrode completing a current path across the power supply to produce an electrostatic field in the gap;

with the conductivity per unit area of each of said electrodes varying from a central zone-to said edges such that the electrostatic potential at the gap surfaces of the electrodes is the same as the electrostatic potential for concentric spherical metal electrodes.

10. An imaging chamber as defined in claim 9 wherein the variation in conductivity per unit area is obtained by varying the thickness of the electrode from the central zone to said edges.

11. An imaging chamber as defined in claim 9 wherein the variation in conductivity per unit area is obtained byvarying the conductivity of the material of the electrode from the central zone to said edges.

12. An imaging chamber as defined in claim 9 wherein the variation in conductivity per unit area is obtained by varying both the thickness of the electrode and the conductivity of the material of the electrode from the central zone to said edges.

13. An imaging chamber as defined in claim 9 wherein the electrostatic potentials 6 and 0 at the gap surfaces of the electrodes are 20 2) 9 z where p is the position on the electrode gap surface, V is the voltage drop across the gap at the gap center, D is the distance from one electrode gap surface to the x-ray-source, d is the distance between electrode gap surfaces, D D+d, and x is the distance ofp from the gap center in polar coordinates for flat electrodes and is the axial distance of p from the gap center for cylindrical electrodes.

' 14. An imaging chamber as defined in claim 9 wherein said electrodes have flat parallel gap surfaces and a central disk of high conductivity material.

15. An imaging chamber as defined in claim 9 wherein said electrodes have concentric cylindrical gap surfaces and a central arcuate strip of high conductivity material. 

1. In an imaging chamber for an x-ray system, the improvement comprising: first and second substantially planar electrodes; means for mounting said electrodes in the chamber in spaced relation defining a gap therebetween; means for connecting a power supply across said electrodes; and means for maintaining along the gap surfaces of said electrodes, electrostatic potentials corresponding to the electrostatic potentials for concentric spherical metal electrodes so that the electric field lines in said gap converge substantially to a point.
 2. An imaging chamber as defined in claim 1 wherein said first and second electrodes are of low conductivity material, with said means for connecting including circuit means for connecting the power supply to the center of said first electrode and to opposite edges of said second electrode, and with said means for maintaining including a resistance connected between opposite edges of said first electrode and the center of said second electrode completing a current path across the power supply to produce an electrostatic field in the gap, with the conductivity per unit area of each of said electrodes varying from a central zone to said edges such that the electrostatic potential at the gap surfaces of the electrodes is the same as the electrostatic potential for concentric spherical metal electrodes.
 3. In an imaging chamber for an x-ray system, the improvement comprising: first and second substantially planar electrodes; means for mounting said electrodes in the chamber in spaced relation defining a gap therebetween; means for connecting a power supply across said electrodes; and means for maintaining along the gap surfaces of said electrodes, electrostatic potentials corresponding to the electrostatic potentials for concentric spherical metal electrodes, with the electrostatic potentials theta 1 and theta 2 at the gap surfaces of the electrodes substantially theta 1 (p1) VgD/d(1+x12/D2) 1/2 theta 2 (p2) VgD''/d (1+x22/D''2) 1/2 where p is the position on the electrode gap surface, Vg is the voltage drop across the gap at the gap center, D is the distance from one electrode gap surface to the x-ray source, d is the distance between electrode gap surfaces, D'' D+d, and x is the distance of p from the gap center in polar coordiNates for flat electrodes and is the axial distance of p from the gap center for cylindrical electrodes.
 4. In an imaging chamber for an x-ray system, the improvement comprising: first and second substantially planar electrodes; means for mounting said electrodes in the chamber in spaced relation defining a gap therebetween; means for connecting a power supply across said electrodes; and means for maintaining along the gap surfaces of said electrodes, electrostatic potentials corresponding to the electrostatic potentials for concentric spherical metal electrodes, with each of said first and second electrodes comprising a plurality of sections of low conductivity material, with each section of different and substantially uniform conductivity, with said means for connecting including circuit means for connecting the power supply to the center of said first electrode and to opposite edges of said second electrode, and with said means for maintaining including a resistance connected between opposite edges of said first electrode and the center of said second electrode completing a current path across the power supply to produce an electrostatic field in the gap, with the conductivity per unit area of each section of said electrodes varying from a central zone to said edges such that the electrostatic potential at the ggap surfaces of the electrodes corresponds stepwise to the electrostatic potential for concentric spherical metal electrodes.
 5. An imaging chamber as defined in claim 1 wherein said electrodes have flat parallel gap surfaces and a central disk of high conductivity material.
 6. An imaging chamber as defined in claim 1 wherein said electrodes have concentric cylindrical gap surfaces and a central arcuate strip of high conductivity material.
 7. In an imaging chamber for an x-ray system, the improvement comprising: first and second substantially planar electrodes; means for mounting said electrodes in the chamber in spaced relation defining a gap therebetween; means for connecting a power supply across said electrodes; and means for maintaining along the gap surfaces of said electrodes, electrostatic potentials corresponding to the electrostatic potentials for concentric spherical metal electrodes, with said electrodes of metal, and with said means for maintaining including first and second dielectric sheets, each of uniform thickness, with said first sheet at said first electrode and said second sheet at said second electrode defining a gap between the sheets, each of said sheets having a dielectric constant varying across the sheet such that the electrostatic potential at the gap surfaces is the same as the electrostatic potential for concentric spherical metal electrodes.
 8. A system as defined in claim 7 wherein each of said sheets comprises a first layer of a first dielectric constant and a second layer of a second dielectric constant, with one of said layers having a maximum thickness at the center thereof and tapering to a minimum thickness at the edges thereof, and with the other of said layers having a complementary thickness.
 9. In an imaging chamber for an x-ray system, the improvement comprising: first and second substantially planar electrodes of low conductivity material; means for mounting said electrodes in the chamber in spaced relation defining a gap there between; means for connecting a power supply to the center of said first electrode and to opposite edges of said second electrode; and a resistance connected between opposite edges of said first electrode and the center of said second electrode completing a current path across the power supply to produce an electrostatic field in the gap; with the conductivity per unit area of each of said electrodes varying from a central zone to said edges such that the electrostatic potential at the gap surfaces of the electrodes is the same as the electrostatic potential for concentRic spherical metal electrodes.
 10. An imaging chamber as defined in claim 9 wherein the variation in conductivity per unit area is obtained by varying the thickness of the electrode from the central zone to said edges.
 11. An imaging chamber as defined in claim 9 wherein the variation in conductivity per unit area is obtained by varying the conductivity of the material of the electrode from the central zone to said edges.
 12. An imaging chamber as defined in claim 9 wherein the variation in conductivity per unit area is obtained by varying both the thickness of the electrode and the conductivity of the material of the electrode from the central zone to said edges.
 13. An imaging chamber as defined in claim 9 wherein the electrostatic potentials theta 1 and theta 2 at the gap surfaces of the electrodes are theta 1 (p1) Vg D/d (1+x12/D2) 1/2 theta 2 (p2) Vg D''/d (1+x22/D''2) 1/2 where p is the position on the electrode gap surface, Vg is the voltage drop across the gap at the gap center, D is the distance from one electrode gap surface to the x-ray source, d is the distance between electrode gap surfaces, D'' D+d, and x is the distance of p from the gap center in polar coordinates for flat electrodes and is the axial distance of p from the gap center for cylindrical electrodes.
 14. An imaging chamber as defined in claim 9 wherein said electrodes have flat parallel gap surfaces and a central disk of high conductivity material.
 15. An imaging chamber as defined in claim 9 wherein said electrodes have concentric cylindrical gap surfaces and a central arcuate strip of high conductivity material. 